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Instead of heels, the kooky singer wore purple lace flats, and despite baring the majority of her legs without an inch left to the imagination, she covered her cleavage in its entirety with a high neckline.

Following their first initial hand-holding outing last month in full view of onlookers, the pair appear to be rather inseparable now.

Living the LA lifestyle: Benji showed off his tattoos as Eliza looked on admirably

Even prior to their PDA in December,
the British singer and Good Charlotte rocker, who once dated Paris
Hilton, had been flirting on Twitter.

Some of his comments appear to have been a play on words of the first letters of Eliza's last name.

On December 6 he wrote: 'Life is GOOD when you DOO what you LOVE'.

She re-tweeted the comment and Benji said the next day: 'Just DOO It,' which is the same motto Eliza has on her Twitter page.

The romance has obviously monopolised over her Twitter love affair, with her last message on Christmas Day simply saying: 'Getting my Baileys on.'

Benji has been a little more vocal, saying yesterday: 'Good day. Good vibes out to everyone keep it positive.'

While she is yet to verbally confirm the news, Eliza has obviously broken up with childhood friend Ollie, who she dated for three-and-a-half years.

Moving fast: Benji was seen driving Eliza around Beverly Hills as they welcomed in the new year together

Inseparable: Benji and Eliza went public with their relationship in December